White vinegar and baking soda
You may need to 'snake' it out. Check with your local hardware or home improvement store for one.
Put down a box of baking soda and add some vinegar until it hits the trap. Hear it fizz and then let it sit for a few hours to work, Rinse with hot water.
I did mine the other day. Took me an hour but the drain work better than ever. Pour one cup of baking soda down the sink and 1 cup of vinegar it will all foam up. Leave for 30 minutes then keep running boiling water down the sink. My water does not get very hot. I boil water in all my pots on the stove and keep putting them down the sink. If you have a plunger use that too. After awhile the fat/ grease blockage will melt away.